Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5732 | C2 | semidirect |
| 3. C3×#486 | C2 | semidirect |
| 4. #5087 | C2 | semidirect |
| 5. #5075 | C2 | semidirect |
| 6. #4780 | C2 | semidirect |
| 7. #4779 | C2 | semidirect |
| 8. #4776 | C2 | semidirect |
| 9. #4770 | C2 | semidirect |
| 10. C4×#204 | C2 | semidirect |
| 11. #4688 | C2 | semidirect |
| 15. C3×C4⋊Q8 | C22 | semidirect |
| 22. C2×#214 | C22 | semidirect |
| 24. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 26. #897 | C22 | semidirect |
| 27. #892 | C22 | semidirect |
| 30. C4×Dic6 | C22 | semidirect |
| 31. C3×#102 | C22 | semidirect |
| 32. C3×#102 | C22 | semidirect |
| 33. C3×C4×C8 | C22 | semidirect |
| 34. #832 | C22 | semidirect |
| 36. (C2×D3)⋊C8 | C22 | semidirect |
| 37. #817 | C22 | semidirect |
| 38. #816 | C22 | semidirect |
| 40. #807 | C22 | semidirect |
| 41. C4⋊(C3⋊C8) | C22 | semidirect |
| 44. #486 | D3 | semidirect |
| 94. C4⋊Q8 | C2×D3 | semidirect |
| 114. #102 | C2×D3 | semidirect |
| 115. #102 | C2×D3 | semidirect |
| 117. C4×C8 | C2×D3 | semidirect |
| 264. C3 | #3324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5732 | 2 |
| #5717 | 2 |
| C3×#486 | 2 |
| #5087 | 2 |
| #5075 | 2 |
| #4780 | 2 |
| #4779 | 2 |
| #4776 | 2 |
| #4770 | 2 |
| C4×#204 | 2 |
| #4688 | 2 |
| #3324 | 3 |